Signals and Systems EE235 Lecture 13 Leo Lam © 2010-2011

Summary: Convolution Draw x() Draw h() Flip h() to get h(-) Shift forward in time by t to get h(t-) Multiply x() and h(t-) for all values of  Integrate (add up) the product x()h(t-) over all  to get y(t) for this particular t value (you have to do this for every t that you are interested in) 2 Leo Lam © 2010-2011

Flip Shift Multiply Integrate y(t) at specific time t0 3 y(t0=3/4)= ? Here t0=3/4 y(t0=3/4)= ? 3/4 Multiply (at all tau) Integrate from –inf to inf. 3 Leo Lam © 2010-2011

y(t) at all t At all t t<0 4 Shift Multiply Integrate The product of these two signals is zero where they don’t overlap 4 Leo Lam © 2010-2011

y(t) at all t At all t 0≤t<1 5 Shift Multiply Integrate Leo Lam © 2010-2011

y(t) at all t At all t 1≤t<2 y(t)=2-t for 1≤t<2 6 Shift Multiply Integrate 6 Leo Lam © 2010-2011

y(t) at all t At all t t≥2 y(t)=0 for t≥2 (same as t<0, no overlap) Shift Multiply Integrate 7 Leo Lam © 2010-2011

y(t) at all t Combine it all 8 y(t)=0 for t<0 and t>2 y(t)=t for 0≤t<1 y(t)=2-t for 1≤t<2 8 Leo Lam © 2010-2011